This leaves a 5 populations problem:
| class | Dropline | Longline |
|---|---|---|
| Big | NA | 24 |
| Medium | 38 | 68 |
| Small | 635 | 12 |
If we assume that within these 5 populations, all boats are the same, we can guess:
| class | fishing_gear | GT | landings |
|---|---|---|---|
| Big | Longline | 42.583333 | 1533.0 |
| Medium | Dropline | 17.210526 | 981.0 |
| Medium | Longline | 26.838235 | 2737.5 |
| Small | Dropline | 8.445669 | 8044.5 |
| Small | Longline | 11.083333 | 199.5 |
You can see that 3 populations really matter the most, Small dropliners, Medium longliners and Big Longiners. They make up 91.2% of the landings.
The biggest population by far, and accounting for about 60% of the landings in 712.
They are organized over 4 ports, with Sumenep and Brondong being the most important.
| Registration Port | Frequency |
|---|---|
| Gili Iyang | 2 |
| PP. Brondong | 163 |
| PP. Tanjung Pandan | 16 |
| Sumenep | 454 |
Assume max 200 days out (4800 hours), no seasonality
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 6.00 10.00 12.00 11.95 13.75 20.00 2
Use formula from hold_size.pdf:
## [1] 1938.128
Which I will round to 1940.
We can also look at their income targets as a function of hold size:
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.2857 0.5179 0.5714 0.6389 0.7143 1.0714 0.0034286
This would mean that approximately 63% of a load is enough to hit the targets.
From the survey, it looks variable costs are about 1 MIL$/day
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.500 1.000 1.000 1.107 1.238 2.500 2
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 20833 41667 41667 46117 51562 104167 2
In fact we can just run a regression and be done with it:
##
## Call:
## lm(formula = `Operational Costs ($/day)` ~ GT, data = survey)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7324 -0.3225 -0.0225 0.1596 5.1775
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.407333 0.119890 3.398 0.00108 **
## GT 0.083038 0.006378 13.020 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8382 on 77 degrees of freedom
## (2 observations deleted due to missingness)
## Multiple R-squared: 0.6876, Adjusted R-squared: 0.6836
## F-statistic: 169.5 on 1 and 77 DF, p-value: < 0.00000000000000022
Which implies, for a GT of 8.5: 46381.4444572
We know (look at trip_info) that on average a small boat goes max distance 236.8060 km from port. Assuming then that fishing costs no gas consumption and that all the gas consumed in the survey is just going back and forth once we get $:
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.4223 0.6493 1.2669 2.5918 1.7683 8.4457 1
Let’s focus on the median (there are some big outliers): 1.2669 l/km
Assuming 13kph (7 knots)
To calibrate.
Assuming folks are explore-exploit-imitate it turns out that most people agree on having a fixed exploration probability:
## No Yes
## 6 18
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 5.00 20.00 25.00 28.33 40.00 50.00 6
A smaller population, accounting for about a third of the small dropline landings is the medium longliners; almost all concentrated in Bajomulyo
| Registration Port | Frequency |
|---|---|
| PP. Bajomulyo | 54 |
| PP. Karangsong | 5 |
| Probolinggo | 9 |
The survey really has only 6 boats that qualify as medium longliners, unfortunately none in 712.
Assume max 200 days out (4800 hours), no seasonality
Again, about 12 days out
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.00 9.75 12.50 11.67 13.00 15.00
Use formula from hold_size.pdf:
## [1] 6906.524
Which I will round to 6900.
None of them has a fixed target income, mostly trying to get a proportion of the operating costs back.
Using the regression (since there are so few respondents): 106929.8444757
We know (look at trip_info) that on average a small boat goes max distance 225.6450 km from port. Assuming then that fishing costs no gas consumption and that all the gas consumed in the survey is just going back and forth once we get $:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.330 1.357 1.440 1.459 1.440 1.773
Let’s focus on the median (there are some big outliers): 1.440 l/km.
This, I think, is a bit too low because we have data on 15-16GT longliners but we want to model 26GT boats instead.
Assuming 13kph (7 knots)
To calibrate.
Assuming folks are explore-exploit-imitate it turns out that most people agree on having a fixed exploration probability:
## No Yes
## 2 4
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 10.0 17.5 20.0 22.5 25.0 40.0 2
There are a few big longliners, they make up only half of the medium longliners landings (and a seventh of the small dropliners) but still significant since they are all concentrated in a few boats.
Unfortunately we only have 4 observations, but all from Probolinggo.
| Registration Port | Frequency |
|---|---|
| PP. Bajomulyo | 21 |
| Probolinggo | 3 |
Assume max 200 days out (4800 hours), no seasonality
These guys stay out for months
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 60 60 60 60 60 60
Use formula from hold_size.pdf (assuming 42 as GT):
## [1] 13498.56
Which I will round to 13500
Using the regression (since there are so few respondents): 162288.3816355
We know (look at trip_info) that on average a small boat goes max distance 528.8952 km from port. Assuming then that fishing costs no gas consumption and that all the gas consumed in the survey is just going back and forth once we get $:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 12.29 13.71 14.65 19.85 20.80 37.81
This is way too high, however it matches Bastardie’s formula 5.9987067 assuming a 1000HP engine (which still feels too powerful, but it’s the only survey answer we got)
Assuming 13kph (7 knots)
To calibrate.
Assuming folks are explore-exploit-imitate it turns out that most people agree on having a fixed exploration probability:
## Yes
## 4
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5.0 6.5 18.5 18.0 30.0 30.0
Let’s pretend 712 can be isolated biologically and socially, such that we have a single fisher landing 13495.5 tonnes a year.
Assuming a low resilience and a guess of average \(\frac {B_{2014}}{K} \approx \frac {B_{2018}}{K} \in [.15,.25]\) we can run Catch-MSY and look at the result. Because of the low spread around \(\frac {B_{t}}{K}\) the result is a quite optimistic outlook with \(K \approx 300,000 t\) and a collapse predicted 8.5 years at current catch levels.
## Possible combinations = 35287
## geom. mean r = 0.262
## r +/- 2 SD = 0.091 - 0.753
## geom. mean k = 298231
## k +/- 2 SD = 185710 - 478928
## geom. mean MSY = 19517
## MSY +/- 2 SD = 8160 - 46679
If we increase uncertainty \(\frac {B_{2014}}{K} \approx \frac {B_{2018}}{K} \in [.10,.30]\) we get a collapse within 4.5 years.
## Possible combinations = 37536
## geom. mean r = 0.296
## r +/- 2 SD = 0.102 - 0.86
## geom. mean k = 188961
## k +/- 2 SD = 135761 - 263009
## geom. mean MSY = 13984
## MSY +/- 2 SD = 5548 - 35244
Let’s start with the optimistic model. We would like the catches in year 2014-2018 to be about right at about 13495.5, properly subdivided between populations. We start the model in 2014, we can get the biomass by stepping backward:
| Biomass | Year |
|---|---|
| 59646.15 | 2018 |
| 62433.49 | 2017 |
| 64808.18 | 2016 |
| 66837.99 | 2015 |
| 68577.93 | 2014 |
This implies \(\frac{B_{2014}}{K} \approx .23\)
We calibrate catchability of the fleet, we can compare simulated and real:
We get more or less the right landings, with small dropliners showing more variability year to year.
If we do a bit of forecast we see that the collapse will not occur in POSEIDON (or at least, not within 10 years). This is because the stock gets depleted enough that CPUE and landings are affected:
Again, assuming in 2018 we are at 20% of \(K\), backtrack to 2014. This time with the pessimistic \(K,r\) combinations
| Biomass | Year |
|---|---|
| 37792.20 | 2018 |
| 43763.18 | 2017 |
| 48766.75 | 2016 |
| 53011.17 | 2015 |
| 56649.73 | 2014 |
That implies that in 2014 the biomass was at about 30% of \(K\). This is a “better” starting point than the optimistic world but it’s only so because the biological parameters are weaker to shocks.
Again, collapse is slower in POSEIDON because agents struggle to keep landings at a constant rate, however in the pessimistic scenario you do get to basically depleted biomass by year 2028.